The invention relates to the field of collision prediction and avoidance of airborne and spaceborne moving vehicles. More particularly, the present invention relates to flight path trajectory conflict prediction and maneuvering avoidance methods for airplanes and spacecraft.
Aircraft conflict prediction and resolution are performed manually by the pilots and air traffic controllers with the help of automated tools. The increase in air traffic is stressing the ability of the Air Traffic Management System to keep aircraft safely separated. Air traffic growth is expected to continue. The FAA Operation Evolution Plan is aimed at supporting a thirty percent overall growth in commercial aviation operations by 2010. Computer controller aids are expected to help relieve air traffic congestion. Such tools also enable free flight, which saves fuel and time. One such controller aid is the User Request Evaluation Tool, which is a conflict probe that looks ahead twenty minutes and helps en route controllers identify potential conflicts above 18,000 feet. Such tools require efficient computational methods to predict conflict.
Aircraft are usually routed between way points with constant altitude, speed and heading. Heading corrections and throttle adjustments are made to prevent each aircraft from deviating too far off course. Nevertheless, navigation errors, uncertainty in winds and aircraft altitude result in position prediction error. These prediction errors were found to be Gaussian and can be represented by error covariance matrices. Between state vector updates, the error covariance matrices grow. Lateral errors are controlled to about xc2x11.0 nmi one sigma. Vertical error is roughly xc2x1100 ft one sigma. Along-track errors grow at a rate of about xc2x115 nautical miles per hour between updates. During climb or decent, position uncertainty increases by an amount that depends on the details of the particular route being studied. Therefore, when aircraft routes are near each other, aircraft position uncertainty results in a probability of the aircraft coming within a specified keep out distance. If the probability value exceeds a threshold, a conflict is declared. A conflict can be resolved by maneuvering one or both of the affected aircraft.
Predicting cumulative collision conflict probability for aircraft with constant velocity is very similar to space vehicle collision probability prediction. For aircraft, the probability of a conflict collision depends on the conflict volume, the relative position error, and the trajectories of the respective aircraft. First, one propagates the aircraft for thirty minutes. Next, coarse screening is performed to identify potential conflicts. Finally, collision conflict probability is predicted. The cumulative collision conflict probability method assumes that the relative velocity is constant and that the relative position error covariance matrix is constant during the encounter. These assumptions are not always valid, because aircraft routing involves turns at way points. In addition, along-track position errors grow between position data updates, The vertical position errors also grow during ascent or descent. Thus, a constant error covariance matrix throughout the encounter between the two aircraft produces uncertain risk of collision. The cumulative collision conflict probability formulation assumes both aircraft were traveling from minus infinity to plus infinity. This assumption can result in small errors in the collision probability. A slight increase in the predicted collision conflict probability could result. For these reasons, a general formulation for collision conflict probability is needed.
A conventional conflict keep-out box is a conflict volume that may be a cylinder 5.0 NMI in radius and 4,000 ft in height for aircraft flying above 29,000 ft. For aircraft flying below 29,000 ft, the cylinder height is reduced to 2,000 ft and a conflict occurs for aircraft with less than 5.0 NMI separation having altitudes that differ by less than xc2x11,000 ft. The cylinder is centered on the flying aircraft and oriented vertically with its height corresponding to altitude. Thus, when an aircraft is predicted to come within 5.0 NMI lateral distance or xc2x12,000 ft vertical distance, a conflict exists. The time of conflict resolution is a tradeoff between efficiency and error uncertainty. When the maneuver is too far in advance, it is efficient and therefore smaller but growth in position uncertainty reduces confidence in the computed collision conflict probability. When the maneuver is not far enough in advance, confidence in the computed collision probability is high but less time is available for the maneuver to avoid the conflict and a larger less efficient maneuver must be made. Thus, there is an optimum maneuver time to resolve a conflict efficiently. The ability to predict conflicts efficiently is needed to help air traffic controllers.
In level flight, the conflict determinations can be partitioned into vertical and horizontal portions because the cylindrical conflict volume is symmetric in the horizontal plane and there is no cross correlation between vertical and horizontal errors. The probability density is integrated from minus infinity to plus infinity along the relative velocity direction. The result is always unity because the probability density is normalized. The resulting two dimensional integral can be partitioned into two separate error function integrals with limits defined by the dimensions of the conflict cylinder. Thus, the conflict probability reduces to the product of two error function integrals.
Vertical and horizontal errors are correlated in the case of non-level flight. In addition, the cylindrical conflict volume takes a more complex shape when the conflict volume is projected to an encounter plane, which is normal to the relative velocity. An approximate solution and a Monte Carlo simulation approach has been proposed to overcome the difficulties of computing conflict probabilities for more complex shapes of the keep-out volume. The computational requirement is significantly greater with the Monte Carlo method. Although the FAA is currently modernizing the traffic control system by increasing automation, effective computerized methods to predict aircraft conflict and avoidance maneuvering are needed.
Collision conflict prediction methods have been used to determine when a spaceborne or airborne vehicle is likely to have a significant collision risk with another object. A contour integration method has already been used on asymmetric space vehicle collision probability and collision probability for space tethers. When there is a significant collision risk, it is then desirable to perform a collision avoidance maneuver prior to the collision time for both aircraft and spacecraft. Spacecraft collision avoidance is also becoming an increasing concern as the number of space objects continues to increase over time. There are currently over 9,500 tracked orbital objects. The need for collision avoidance maneuvers is correspondingly increasing as the number of operational satellites and associated debris objects increase. The narrow altitude bands associated with communication satellite constellations in both low earth orbit and geosynchronous earth orbit requires improved collision prediction and avoidance methods because satellites occupying the same altitude range have increased risk of collision. The collision hazard posed by debris and other operational satellites has been increasing to the point where collision avoidance maneuvers should be considered as a means to mitigate the collision risk. The increasing collision hazard is forcing manned vehicles to perform unwanted collision avoidance maneuvers. Such maneuvers are disruptive to mission operations. For example, the Space Shuttle performs a maneuver, when the predicted miss distance is less than two kilometers radially, five kilometers in-track and two kilometers out-of-plane. The International Space Station has already performed two collision avoidance maneuvers based on collision probability predictions. Collision avoidance maneuvers for space vehicles reduce vehicular life span due to propellant consumption while additional thruster firings increase the potential for propulsion system failure. The decision to perform a collision avoidance maneuver is based on a cost-risk analysis that requires a quantifiable measure of risk. Unlike a keep-out box criterion, collision probability provides the needed quantification of risk. Collision probability can be weighed against the propellant consumed and shortened operational life span of the space vehicle. The value of the space asset can be used to establish a collision risk threshold. Because the amount of propellant is directly related to an operational lifetime and revenue of a satellite, maneuvers should be performed in the most efficient and effective manner possible. This requires searching a four-dimensional space for an optimal solution. This space consists of the time of application, velocity magnitude and direction, right ascension and declination, of the applied maneuver. Computational efficiencies in propagation, collision probability calculation and optimization are required to allow sufficient time for maneuver planning.
The maneuver is made to reduce the collision risk to an acceptable level. The most effective maneuver is one that requires minimum maneuver velocity and associated propellant. There are three components necessary to determine the most effective maneuver: maneuver time, maneuver direction, and maneuver magnitude. These components need to be determined expeditiously so that enough time is allowed for performing operational tasks required to implement the maneuver. Hence, there exists a need to timely determine the optimal maneuver for avoidance of a pending collision. Numerical methods have been used for conflict avoidance and maneuvering, but the numerical method often required more time to predict a collision and maneuver than is available during a pending collision. These and other disadvantages are solved or reduced using the invention.
An object of the invention is to provide a method for predicting potential collisions.
Another object of the invention is to reduce risk to a subject object from collision with one or more target objects.
An object of the invention is to provide a method for screening target objects for those that come within an approach distance to a subject object for indicating a possible collision conflict.
Another object of the invention is to provide a method for determining a conjunction between a target object and a subject object when the separation distance is within a critical distance through high fidelity trajectory propagation for indicating a probable collision conflict.
Yet another object of the invention is to provide a method for determining a collision conflict probability of a collision between a subject object and a target object through high fidelity trajectory propagation, through coordinate rotation and scaling based on error covariance matrices, and through contour integration.
Another object o f the invention is to provide a method for determining an optimum maneuver including a maneuver time, maneuver direction, and maneuver magnitude of a maneuvering subject object for avoiding a collision with a target object through a gradient method and a root finding method.
The invention relates to collision prediction and collision avoidance maneuvering. The invention method determines risk of a potential collision between a subject object and a target object, and determines an optimum maneuver to avoid potential collision. The subject object may be an aircraft, an orbiting spacecraft, a launch spacecraft, or a free space traveling spacecraft. The target object may be one of many target objects that may also be an aircraft, an orbiting spacecraft, al launch spacecraft, a free space traveling spacecraft, space debris, or airborne debris.
The method first determines when the subject object will come within a large approach distance for screening target objects that have an impossible collision conflict with the subject object. For those target objects that do not have an impossible collision conflict, the method then determines whether the closest approach separation distance between the subject object and the target object will be less than a critical distance for determining a conjunction through trajectory propagations. Conjunction determinations use high-fidelity time-stepped trajectory propagation.
When it is determined that a target object will have a conjunction with the subject object, then the method determines the collision probability between the subject object and the target object. The collision probability is a risk of a potential collision. The collision probability determination uses an error covariance matrix that is transformed to an encounter frame by rotation and scaling. In the encounter frame, a contour integration method is used for efficient computation of collision conflict probability. When a target object will have a collision conflict probability with the subject object above a predetermined collision conflict probability threshold, that is, above a predetermined risk value, then a maneuver may be executed for collision avoidance.
When the subject object will have collision conflict probability above the predetermined collision conflict probability, indicating a need for maneuver avoidance, the method then determines an optimum maneuver, in terms of maneuver direction, maneuver magnitude, and maneuver time so as to reduce the collision conflict probability below the predetermined probability for reducing risk of collision. The direction and magnitude of the maneuver velocity is found in two steps. The direction is found by using a gradient method, which determines the maneuver direction that results in the largest reduction in collision probability for a given maneuver velocity magnitude. Once the direction is found, the maneuver magnitude is found by using a search method, such as a Secant root or Newton root search method that lowers the collision probability to below the collision probability threshold. A maneuver choice can be made from the selection of optimal maneuvers from maneuver options. When a maneuver is required, a maneuver duration is selected for indicating possible maneuver times prior to the conjunction. For each time step during the maneuver duration, the optimum maneuver is found that reduces the collision probability. The optimum maneuver is determined in a computationally efficient manner that requires negligible amounts of time. This efficient computation allows sufficient time for planning the maneuvers.
The method uses various processes, including conjunction determinations through trajectory propagation, collision probability prediction through coordinate rotation and scaling based on error covariance matrices, and numerical searching for optimum avoidance maneuvers. Significantly, the collision probability calculation is performed using an enhanced contour integration method for rapid computation. The maneuver avoidance method determines the effect of a vehicular maneuver on the collision probability by propagating the vehicle from the potential collision time backwards to the maneuver time, and then applying the maneuver and propagating the vehicle forward in time to the potential collision time. Significantly, the maneuvering direction is determined using a gradient method. The propagation is analytically performed using either conventional Keplerian two-body mechanics or high fidelity trajectory propagation.
The method is applicable to aircraft having level, turning, ascending and descending flight paths, and spacecraft having orbital flight paths, launch vehicles having launch paths, or spacecraft having free space flight paths. Collision probability for aircraft has inputs including altitude position, speed and direction, and safety keep-out volumes. Spacecraft use a hard-body volumes for collision probability and aircraft use a keep-out volume for conflict prediction, but herein, both nomenclatures are mathematically treated the same for collision probability computations.
Collision probability prediction for spacecraft has inputs including the respective state vectors, error covariance matrices, and physical sizes of the subject and target objects with the sizes being used as safety keep-out volumes. Because the relative velocity of orbital objects at the closest approach is very large compared to the relative accelerations, the relative velocity is considered constant during the encounter period of closest approach. When more than one collision is possible for the subject object, such as for orbital bodies having cyclic orbits, the cumulative collision probability is used in place of the single collision probability. The cumulative collision probability is the sum of collision probability for each potential collision. The method enhances the ability to predict potential collisions and to determine avoidance maneuvers in a timely manner so as to avoid collision. This would enable operational collision risk of aircraft and spacecraft to be reduced in an automated manner. These and other advantages will become more apparent from the following detailed description of the preferred embodiment.